Câu 4 : so sánh phân số bằng cách nhanh nhất :
C)\(\dfrac{27}{26}\)và \(\dfrac{38}{37}\)
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\(\dfrac{27}{86}\) < \(\dfrac{27}{81}\) = \(\dfrac{1}{3}\) = \(\dfrac{9}{27}\) < \(\dfrac{25}{27}\)
Vậy \(\dfrac{27}{86}\) < \(\dfrac{25}{27}\)
a: \(\frac{11}{32}>\frac{11}{33}=\frac13\)
\(\frac13=\frac{16}{48}>\frac{16}{49}\)
Do đó: \(\frac{11}{32}>\frac{16}{49}\)
b: \(\frac{46}{71}<\frac{46}{69}=\frac23\)
\(\frac23=\frac{38}{57}<\frac{38}{55}\)
Do đó: \(\frac{46}{71}<\frac{38}{55}\)
c: \(\frac{12}{47}>\frac{12}{48}=\frac14\)
\(\frac14=\frac{29}{116}>\frac{29}{117}\)
Do đó: \(\frac{12}{47}>\frac{29}{117}\)
d: \(\frac{18}{53}>\frac{18}{54}=\frac13\)
\(\frac13=\frac{34}{102}>\frac{34}{103}\)
Do đó: \(\frac{18}{53}>\frac{34}{103}\)
a) \(\dfrac{27}{35}>\dfrac{19}{35}>\dfrac{19}{41}\)
\(\Rightarrow\dfrac{27}{35}>\dfrac{19}{41}\)
b) \(\dfrac{120}{121}< \dfrac{120+1}{121+1}=\dfrac{121}{122}\)
\(\Rightarrow\dfrac{120}{121}< \dfrac{121}{122}\)
Ta có: \(\frac{27}{26}\)= \(\frac{27\times37}{26\times37}\)= \(\frac{999}{962}\).
\(\frac{38}{37}\)= \(\frac{38\times26}{37\times26}\)= \(\frac{988}{962}\).
Mà \(\frac{999}{962}\)> \(\frac{988}{962}\).
=> \(\frac{27}{26}\)> \(\frac{38}{37}\).
Cách 1:
\(\dfrac{3}{4}=\dfrac{9}{12}\)
\(\dfrac{4}{3}=\dfrac{16}{12}\)
Do đó \(\dfrac{3}{4}< \dfrac{4}{3}\)
Cách 2:
\(\dfrac{3}{4}< 1\)
\(1< \dfrac{4}{3}\)
Do đó \(\dfrac{3}{4}< \dfrac{4}{3}\)
\(-------\)
Cách 1:
\(\dfrac{11}{8}=\dfrac{55}{40}\)
\(\dfrac{7}{10}=\dfrac{28}{40}\)
Do đó \(\dfrac{11}{8}>\dfrac{7}{10}\)
Cách 2:
\(\dfrac{11}{8}>1\)
\(1>\dfrac{7}{10}\)
Do đó \(\dfrac{11}{8}>\dfrac{7}{10}\)
c) \(\dfrac{27}{26}\)và\(\dfrac{38}{37}\)
Ta có: \(\dfrac{27}{26}=1+\dfrac{1}{26}\); \(\dfrac{38}{37}=1+\dfrac{1}{37}\)
Vì \(\dfrac{1}{26}>\dfrac{1}{37}\) nên \(\dfrac{27}{26}>\dfrac{38}{37}\)
c: \(\dfrac{27}{26}-1=\dfrac{1}{26}\)
\(\dfrac{38}{37}-1=\dfrac{1}{37}\)
mà \(\dfrac{1}{26}>\dfrac{1}{37}\)
nên \(\dfrac{27}{26}>\dfrac{38}{37}\)